Let's see, Plato may show up and set us straight.
There are 6 steps from beginning to end and 3 across. If our start is (0,0), then the end would have step (6,3)
A block walker gets to (n,k) from either corner (n-1,k) or (n-1,k-1)
To get to corner (6,3) we go to (5,3) and goes left to (6,3) or goes to (5,2) and turns right to (6,3).
Thus the number of routes is (n-1,k-1)+(n-1,k)